Your inputs

One swing, eight levels

Swing high

The swing’s highest price, from $0.0001 through $10 million.

Swing low

The swing’s lowest price — it must sit below the swing high.

Your inputs are calculated locally and are not stored.

Golden-ratio level (61.8%)$119.10

After an up swing from $100.00 to $150.00, price retraces 61.8% of the range at $119.10.

23.6%: $138.20
38.2%: $130.90
50%: $125.00
61.8%: $119.10
78.6%: $110.70
Ext 127.2%: $163.60
Ext 161.8%: $180.90
Ext 261.8%: $230.90

Formula & methodology

How Fibonacci levels are calculated

A retracement level marks where a partial pullback of the swing would stall. For an up swing the calculator measures the range from low to high, then steps down from the high by each ratio: retracement price = High − (High − Low) × ratio. For a down swing the math is mirrored — levels step up from the low. Extensions use the same range but project beyond the swing, marking where a move that continues past the old extreme might reach.

The ratio family comes from the Fibonacci sequence’s limit ratio φ ≈ 1.618: 61.8% is 1/φ, 38.2% is 1/φ², and 23.6% is 1/φ³. The 50% level is a trader convention rather than a Fibonacci number — it survives on the charts because half-back pullbacks are so common.

Retracement = High − (High − Low) × Ratio

High: Swing high price
Low: Swing low price
Ratio: Fibonacci ratio, 0.236 through 0.786
Extension: Low + (High − Low) × ratio above 1, beyond the swing

Worked example

An up swing from $100 to $150

Suppose a stock rallies from a $100 swing low to a $150 swing high — a $50 range. The shallow 23.6% retracement sits at $138.20 and the 38.2% level at $130.90. The conventional 50% level lands at $125.00, the golden-ratio 61.8% retracement at $119.10, and the deep 78.6% level at $110.70. If the rally resumes and clears $150, the 127.2% extension projects $163.60 and the 161.8% extension $180.90.

This is an educational calculation based only on the values you provide. It does not look up live prices, and it is not trading advice.

Assumptions

What this calculator assumes

Levels are geometry, not prophecy — they divide the swing mathematically and carry no guarantee that price will react at any of them.
Fibonacci levels are most useful in confluence with other evidence: prior support and resistance, moving averages, or volume, not as standalone signals.
Direction flips the anchor — up swings retrace down from the high, down swings retrace up from the low — so labeling the swing correctly matters as much as the prices.
This is an educational charting aid, not trading or investment advice.

Common questions

Fibonacci retracement FAQ

Why 61.8%?

61.8% is the inverse of the golden ratio φ ≈ 1.618, the value the ratio of consecutive Fibonacci numbers converges toward. It is the most-watched retracement on the ladder: traders treat a pullback that holds near 61.8% as a trend that bent without breaking, which is why the calculator headlines that level.

What is the difference between a retracement and an extension?

Retracements sit inside the swing — they mark partial pullbacks of the original move, from a shallow 23.6% to a deep 78.6%. Extensions sit beyond the swing, projecting where price might travel if the move resumes and passes its old extreme. Traders lean on retracements for entries and extensions for profit targets.

Do Fibonacci levels work?

The honest answer: the evidence is mixed. There is no physical law forcing price to respect a ratio, and academic studies find little standalone predictive power. But widely watched levels create real order flow — enough traders place bids and stops around them to make reactions self-fulfilling at times. Use them as context alongside other analysis, not as a system.

Primary sources

Sources and review notes

Investor.gov (SEC) — Technical analysis glossary
John J. Murphy, Technical Analysis of the Financial Markets — retracement chapters

Methodology last checked Jul 16, 2026. Formula implementation is covered by deterministic unit tests. No financial professional review is claimed yet.